Pulleys for endless belt drive systems, whether flat pulleys, wedge pulleys, poly-V-ribbed pulleys, or the like, typically come in one of three basic forms: solid, profiled, or arm design. Smaller pulleys may be designed as solid pulleys, where an annular disk having approximately the same width as the pulley connects the hub to the outer rim. Larger pulleys are frequently designed as profiled or webbed pulleys, where an annular portion or web that is substantially narrower than the width of the pulley connects the hub to the outer rim. Still larger pulleys (or pulleys where the volume and/or weight of the pulley material is critical) tend to be designed as arm design pulleys, where a plurality of distinct and outwardly radiating arms, which may be designed as spokes, struts, ribs, or the like, connect the hub to the outer rim. The arms are usually, but not necessarily, separated from each other by inter-arm voids.
Arm design pulleys may be preferred for efficiency considerations, but create additional dynamic behaviors in high-capacity drive systems due to variations in the structural characteristics of the pulley rim. The belts in belt drive systems are tensioned so that friction between the outer rim of a pulley and the flanks and/or faces of the belt can efficiently transmit power within the system. However, belt tension tends to compress each pulley, at least along the pulley's winding arc, which slightly reduces the radius of the engaged running surface of the outer rim. In a solid or profiled pulley the structural characteristics of the outer rim and belt running surface remain essentially the same around the entire circumference of the pulley. Consequently, the outer rim can be considered to be rotationally uniform, and belt entry and exit conditions can frequently be considered to be quasi-static. Conversely, in an arm design pulley the portions of the outer rim that are in close proximity to the arms will be stiffer than the portions of the outer rim that bridge between arms, or, in other words, the running surface proximate to an arm will be comparatively resistant to compressive deformation, while the running surface remote from an arm will be comparatively susceptible to flexural deformation. Consequently, the outer rim is not rotationally uniform but rather rotationally variable, with changes in belt entry and exit conditions potentially generating audible vibrations in the pulley and/or the belt drive system. This variation in stiffness can be reduced by increasing the thickness of the outer rim, but at the cost of adding substantially more material to the pulley.
The dynamic behaviors of an arm design pulley can materially and undesirably contribute to the operating noise of the belt drive system. The arms in such a pulley most conventionally radiate outward from the hub to the outer rim, are structurally identical, and are separated from adjacent arms by equal angular spacings, so that the pulley exhibits n-fold rotational symmetry (with n being the number of arms in the pulley). Noise attributable to the aforementioned variation in the structural characteristics of the pulley, and amplified by the regular nature of that variation about the circumference of the outer rim, can manifest as an energetic peak or peaks in the noise spectrum of the belt drive system. The frequencies involved can be described by the following: frequency (Hz)=(order*RPM)/60, where the term “order” represents, for any particular structural characteristic or logically related class of characteristics of concern, the number of regularly recurring variations about the circumference of the pulley rim, and RPM is the rotational speed of the pulley. The structural characteristic, and thus “order,” principally addressed herein is the number of arms connecting a hub to an outer rim, but other structural characteristics may be of concern, and may be addressed by the techniques described herein. For example, pulleys for endless belt drive systems are frequently manufactured from thermoplastics, thermosetting plastics, or moldable plastic composites, however the molding process can create unwanted variations in the running surface of the outer rim. Material in sections of the outer rim overlying or proximate to an arm will not flow, crystalize, and/or set in the same manner as material in sections of the outer rim bridging between arms. The Applicants have observed that the radius of the running surface of molded arm design pulleys tends to decrease or shrink proximate each arm during cooling due to the relative thickness of the underlying material. This regular variation in the running surface of the finished product can create or further exacerbate an order-driven energetic peak or peaks in the noise spectrum of the belt drive system, particularly during seating of the flanks and/or faces of the belt on the outer rim.
The Applicants have determined that operating noise attributable to variability in the structural characteristics of the outer rim and belt running surface, and specifically the amplitude of distinct peaks in the noise spectrum attributable to such variability, can be diminished by eliminating the lateral symmetry that is conventionally found in arm design pulleys. Sets of laterally asymmetric supporting arms can be offset from each other to create out of phase or intermittent vibrations which destructively interfere with simple modes of vibration caused by such variability. This operating noise can also be diminished by reducing or eliminating the rotational symmetry that is conventionally found in arm design pulleys. The outer ends of laterally symmetric arms (or laterally asymmetric sets of arms) can be separated by varying arcuate spacings about the outer rim to reduce the amplitude of any single mode of vibration, and pitch sequences can be selected to both pseudo-randomize the angular variability of the outer rim and reduce or eliminate the rotational symmetry of the pulley. Combinations of lateral asymmetry and reduced rotational symmetry can introduce further disorder into the running surface of an arm design pulley to further disrupt simple modes vibration. Accordingly, new low-noise pulley designs and new methods of constructing low-noise pulleys are presented.